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Register a new userAssessing the accuracy of quantum Monte Carlo and density functional theory for energetics of small water clusters
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We present a detailed study of the energetics of water clusters (H$_2$O)$_n$ with $n le 6$, comparing diffusion Monte Carlo (DMC) and approximate density functional theory (DFT) with well converged coupled-cluster benchmarks. We use the many-body decomposition of the total energy to classify the errors of DMC and DFT into 1-body, 2-body and beyond-2-body components. Using both equilibrium cluster configurations and thermal ensembles of configurations, we find DMC to be uniformly much more accurate than DFT, partly because some of the approximate functionals give poor 1-body distortion energies. Even when these are corrected, DFT remains considerably less accurate than DMC. When both 1- and 2-body errors of DFT are corrected, some functionals compete in accuracy with DMC; however, other functionals remain worse, showing that they suffer from significant beyond-2-body errors. Combining the evidence presented here with the recently demonstrated high accuracy of DMC for ice structures, we suggest how DMC can now be used to provide benchmarks for larger clusters and for bulk liquid water.
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We use coupled-cluster quantum chemical methods to calculate the energetics of molecular clusters cut out of periodic molecular hydrogen structures that model observed phases of solid hydrogen. The hydrogen structures are obtained from Kohn-Sham density functional theory (DFT) calculations at pressures of 150, 250 and 350 GPa, which are within the pressure range in which phases II, III and IV are found to be stable. The calculated deviations in the DFT energies from the coupled-cluster data are reported for different functionals, and optimized functionals are generated which provide reduced errors. We give recommendations for semi-local and hybrid density functionals that are expected to accurately describe hydrogen at high pressures.
Density functional theory (DFT) is widely used in surface science, but gives poor accuracy for oxide surface processes, while high-level quantum chemistry methods are hard to apply without losing basis-set quality. We argue that quantum Monte Carlo techniques allow these difficulties to be overcome, and we present diffusion Monte Carlo results for the formation energy of the MgO(001) surface and the adsorption energy of H$_2$O on this surface, using periodic slab geometry. The results agree well with experiment. We note other oxide surface problems where these techniques could yield immediate progress.
Density-functional theory (DFT) has revolutionized computational prediction of atomic-scale properties from first principles in physics, chemistry and materials science. Continuing development of new methods is necessary for accurate predictions of new classes of materials and properties, and for connecting to nano- and mesoscale properties using coarse-grained theories. JDFTx is a fully-featured open-source electronic DFT software designed specifically to facilitate rapid development of new theories, models and algorithms. Using an algebraic formulation as an abstraction layer, compact C++11 code automatically performs well on diverse hardware including GPUs. This code hosts the development of joint density-functional theory (JDFT) that combines electronic DFT with classical DFT and continuum models of liquids for first-principles calculations of solvated and electrochemical systems. In addition, the modular nature of the code makes it easy to extend and interface with, facilitating the development of multi-scale toolkits that connect to ab initio calculations, e.g. photo-excited carrier dynamics combining electron and phonon calculations with electromagnetic simulations.
Cubic hafnia (HfO$_2$) is of great interest for a number of applications in electronics because of its high dielectric constant. However, common defects in such applications degrade the properties of hafina. We have investigated the electronic properties of oxygen vacancies and nitrogen substitution in cubic HfO$_2$ using first principles calculations based on density functional theory (DFT) and many-body diffusion Monte Carlo (DMC) methods. We investigate five different charge defect states of oxygen vacancies, as well as substitutional N defects which can lead to local magnetic moments. Both DMC and DFT calculations shows that an oxygen vacancy induces strong lattice relaxations around the defect. Finally, we compare defect formation energies, charge and spin densities obtained from DMC with results obtained using DFT. While the obtained formation energies from DMC are 0.6~eV -- 1.5~eV larger than those from GGA+U, the agreement for the most important defects, neutral and positively charged oxygen vacancies, and nitrogen substitutional defect, under oxygen-poor conditions are in reasonably good agreement. Our work confirms that nitrogen can act to passivate cubic hafnia for applications in electronics.
We have applied the many-body ab-initio diffusion quantum Monte Carlo (DMC) method to study Zn and ZnO crystals under pressure, and the energetics of the oxygen vacancy, zinc interstitial and hydrogen impurities in ZnO. We show that DMC is an accurate and practical method that can be used to characterize multiple properties of materials that are challenging for density functional theory approximations. DMC agrees with experimental measurements to within 0.3 eV, including the band-gap of ZnO, the ionization potential of O and Zn, and the atomization energy of O$_2$, ZnO dimer, and wurtzite ZnO. DMC predicts the oxygen vacancy as a deep donor with a formation energy of 5.0(2) eV under O-rich conditions and thermodynamic transition levels located between 1.8 and 2.5 eV from the valence band maximum. Our DMC results indicate that the concentration of zinc interstitial and hydrogen impurities in ZnO should be low under n-type, and Zn- and H-rich conditions because these defects have formation energies above 1.4 eV under these conditions. Comparison of DMC and hybrid functionals shows that these DFT approximations can be parameterized to yield a general correct qualitative description of ZnO. However, the formation energy of defects in ZnO evaluated with DMC and hybrid functionals can differ by more than 0.5 eV.
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